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fricas
zerosOf(7-5*x+5*x^2-x^3,x)

\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[ \%x 0, \:{{-{\sqrt{-{3 \ {{\%x 0}^{2}}}+{{10}\  \%x 0}+ 5}}- \%x 0 + 5}\over 2}, \: \right.
\
\
\displaystyle
\left.{{{\sqrt{-{3 \ {{\%x 0}^{2}}}+{{10}\  \%x 0}+ 5}}- \%x 0 + 5}\over 2}\right] 
(1)
Type: List(Expression(Integer))

fricas
simplify((6+(-1+x)^2*(-2+(-3+x)*(-1+x))-6*x)/(-1+x))

\label{eq2}{{x}^{3}}-{5 \ {{x}^{2}}}+{5 \  x}- 7(2)
Type: Expression(Integer)

fricas
factor(-(-x^2+y^2)*(z-x)+(-x^2+z^2)*(y-x))

\label{eq3}{\left(y - x \right)}\ {\left(z - y \right)}\ {\left(z - x \right)}(3)
Type: Factored(Polynomial(Integer))
fricas
simplify(((-(-w+y)*(-w^2+x^2)+(-w^2+y^2)*(x-w))*(-(-w^3+x^3)*(z-w)+(-w^3+z^3)*(x-w))-((-w^3+y^3)*(x-w)-(-w+y)*(-w^3+x^3))*((-w^2+z^2)*(x-w)-(-w^2+x^2)*(z-w)))/(x-w))

\label{eq4}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {{y}^{2}}}+{{\left(-{{x}^{2}}+{{w}^{2}}\right)}\  y}+{w \ {{x}^{2}}}-{{{w}^{2}}\  x}\right)}\ {{z}^{3}}}+ 
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {{y}^{3}}}+{{\left({{x}^{3}}-{{w}^{3}}\right)}\  y}-{w \ {{x}^{3}}}+{{{w}^{3}}\  x}\right)}\ {{z}^{2}}}+ 
\
\
\displaystyle
{{\left({{\left({{x}^{2}}-{{w}^{2}}\right)}\ {{y}^{3}}}+{{\left(-{{x}^{3}}+{{w}^{3}}\right)}\ {{y}^{2}}}+{{{w}^{2}}\ {{x}^{3}}}-{{{w}^{3}}\ {{x}^{2}}}\right)}\  z}+ 
\
\
\displaystyle
{{\left(-{w \ {{x}^{2}}}+{{{w}^{2}}\  x}\right)}\ {{y}^{3}}}+{{\left({w \ {{x}^{3}}}-{{{w}^{3}}\  x}\right)}\ {{y}^{2}}}+ \
\
\displaystyle
{{\left(-{{{w}^{2}}\ {{x}^{3}}}+{{{w}^{3}}\ {{x}^{2}}}\right)}\  y}
(4)
Type: Expression(Integer)
fricas
expand((z-y)*(z-x)*(z-w)*(y-x)*(y-w)*(x-w))

\label{eq5}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {{y}^{2}}}+{{\left(-{{x}^{2}}+{{w}^{2}}\right)}\  y}+{w \ {{x}^{2}}}-{{{w}^{2}}\  x}\right)}\ {{z}^{3}}}+ 
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {{y}^{3}}}+{{\left({{x}^{3}}-{{w}^{3}}\right)}\  y}-{w \ {{x}^{3}}}+{{{w}^{3}}\  x}\right)}\ {{z}^{2}}}+ 
\
\
\displaystyle
{{\left({{\left({{x}^{2}}-{{w}^{2}}\right)}\ {{y}^{3}}}+{{\left(-{{x}^{3}}+{{w}^{3}}\right)}\ {{y}^{2}}}+{{{w}^{2}}\ {{x}^{3}}}-{{{w}^{3}}\ {{x}^{2}}}\right)}\  z}+ 
\
\
\displaystyle
{{\left(-{w \ {{x}^{2}}}+{{{w}^{2}}\  x}\right)}\ {{y}^{3}}}+{{\left({w \ {{x}^{3}}}-{{{w}^{3}}\  x}\right)}\ {{y}^{2}}}+ \
\
\displaystyle
{{\left(-{{{w}^{2}}\ {{x}^{3}}}+{{{w}^{3}}\ {{x}^{2}}}\right)}\  y}
(5)
Type: Polynomial(Integer)




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